Bi-objective Branch-and-Cut Algorithms Based on LP Relaxation and Bound Sets

Branch-and-bound for bi-objective integer programming

In Pareto bi-objective integer optimization the optimal result corresponds to a set of nondominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions, and cutting plane generation taking advantage of integer objective values. The developed algorithm is applied to the bi-objective team ori...

Branch-and-Cut Algorithms

Branch and Cut Algorithms

is the objective function to be optimized over P . Whenever all variables in (1.1) are restricted to be integral, the problem is known as a linear integer programming (IP) problem. Conversely, a pure linear programming (LP) problem results when all variables in (1.1) are restricted to be real valued. As is frequently the case for MIP, instead of attempting to optimize (1.3) directly over P , it...

Branch-and-cut Algorithms for Integer Programming, Branch-and-cut

Branch-and-cut methods are exact algorithms for integer programming problems. They consist of a combination of a cutting plane method with a branch-and-bound algorithm. These methods work by solving a sequence of linear programming relaxations of the integer programming problem. Cutting plane methods improve the relaxation of the problem to more closely approximate the integer programming probl...

Multi-objective branch-and-bound. Application to the bi-objective spanning tree problem

This paper focuses on a multi-objective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multi-objective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that a node in the search tree can be discarded i...